"In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics, where mathematics is developed primarily for its own sake. Thus, the activity of applied mathematics is vitally connected with research in pure mathematics." -wikipedia
Pure and Applied Math curriculum, what is the difference? well in my opinion traditionally they differ in courses taken... pure math majors usually take courses in modern algebra, advanced geometry and topology, advanced analysis (real and complex), number theory perhaps, etc... applied math students usually take courses involving mathematical modeling (probably in the field of finance, biology, physics, management science, etc)...
also most of the time they differ in the concentration of research... pure math build theorems while applied math build models... but this is the issue: shall we limit our researches in university as that? pure math majors do not lose their name as pure math majors if they do research building models since (1) they still took pure math courses which makes the case different from the applied math curriculum; (2) in building models, you can build new field in math, for example: coding theory, homogenization, automata, etc. (3) we should not limit our pure math majors to be boxed and we should give them freedom in doing research, thus makes them more flexible and relevant in society... basic research alone is important but basic research + applications is better I believe, especially if we look at what our country really needs. Advisers of pure math majors should guide their students to do basic research and hope with applications such that their skills as math major will not be compromised.
and lastly, division between pure and applied math has advantages, especially in what majors focus on --- it is important to do basic science. but we should not totally divide the two, especially in research --- still collaboration is one of the best things happening in science and we should take this opportunity. pure math should do basic research (60-80% of the research) such that we are hopeful that what they do have applications (40-20% of the research). in addition, applied math should not be limited in just applying existing math techniques but they be given freedom to build their own theorems and techniques, well as what they say --- applied math is math + something else. wag sana tayo pahuli sa mga universities sa ibang bansa...
we should not just be contented with the argument that if a pure math student wants to do research with applications then he should shift to applied math curriculum... this violates the freedom of the student to choose --- he still wants to take pure math courses but the only difference is he wants to build theorems that have applications or have been motivated by real world situations.
>>> leave the hard core pure math to PhDs... undergrad should be flexible in their research...